Recurring DNA copy-number alterations (CNAs) have been recognized as a hallmark of cancer for >100 years, yet what these alterations imply about a tumor's pathogenesis and a patient's diagnosis, prognosis, and treatment remains poorly understood. This is despite the growing number of large-scale multidimensional datasets recording different aspects of a single disease, e.g., in the Cancer Genome Atlas (TCGA), and due to a fundamental need for mathematical frameworks that can create one coherent model from such multiple datasets arranged in multiple tensors of matched columns, e.g., patients, platforms, and tissues, but independent rows, e.g., probes. For example, our recent comparative modeling (by using a data-driven two-matrix spectral decomposition) of patient-matched glioblastoma (GBM) brain tumor and normal blood genomic profiles from TCGA (arranged in two matrices, of matched columns but independent rows) uncovered a previously unknown global pattern of tumor-exclusive CNAs that is correlated with, and possibly causally related to, GBM survival and response to chemotherapy. The data had been publicly available since 2008, but this signature remained unknown until we applied our comparative modeling in 2012. Survival analyses showed, and computationally validated, that the signature performs better than, and is statistically independent of, age, the best indicator of GBM survival for >50 years, and existing GBM pathology laboratory tests. A new test for GBM based upon this signature is pending an experimental re-validation at the Associated Regional and University Pathologists (ARUP) Laboratories, Inc., a nonprofit reference laboratory of the Department of Pathology at the University of Utah. In this NCI U01 project, our multidisciplinary team of researchers from the Departments of Bioengineering, Mathematics, and Pathology, the Scientific Computing and Imaging (SCI) Institute, and the Huntsman Cancer Institute (HCI) at the University of Utah, aims to (i) define, and study the properties of data- driven multi-tensor spectral decompositions; (ii) use these to model patient-, platform-, and tissue-matched but probe-independent TCGA genomic profiles, and gain biological and medical insights into the genotype- phenotype relations in lower-grade astrocytoma (LGA) brain cancer, ovarian serous cystadenocarcinoma (OV), and lung squamous cell carcinoma; and (iii) enable translation of these insights into pathology laboratory tests, by experimentally testing the computational predictions of the existing GBM model, as well as the novel LGA and OV models by using Utah samples. Ultimately, this project will bring physicians a step closer to one day being able to predict and control the progression of cell division and cancer as readily as NASA engineers plot the trajectories of spacecraft today.